OFFSET
1,2
COMMENTS
The decompositions need not be unique. E.g., for a(7) either 1/12 or 1/20 + 1/30 may be used in the decomposition indifferently.
For prime numbers p and any fixed epsilon < 1, a(p) > epsilon*p*log(p) for all sufficiently large p.
LINKS
Jon E. Schoenfield, All unitary decompositions (listed in lexicographic order) for n = 1..30. (Decompositions up to n = 18 originally found by J. Múgica.)
Javier Múgica, Values of a(n)/n.
EXAMPLE
1 = 1/3 + 1/4 + 1/6 + 1/10 + 1/12 + 1/15, and there is no such decomposition starting at 1/3 and having a greatest denominator smaller than 15, so a(3)=15.
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Javier Múgica, Nov 06 2017
EXTENSIONS
a(18)-a(24) from Jon E. Schoenfield, Dec 22 2019
a(25)-a(56) from Jon E. Schoenfield, Jan 01 2020
STATUS
approved